Geometry With An Introduction To Cosmic Topology

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Geometry with an Introduction to Cosmic Topology

Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
ISBN 13 : 0763754579
Total Pages : 255 pages
Book Rating : 4.7/5 (637 download)

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Book Synopsis Geometry with an Introduction to Cosmic Topology by : Michael P. Hitchman

Download or read book Geometry with an Introduction to Cosmic Topology written by Michael P. Hitchman and published by Jones & Bartlett Learning. This book was released on 2009 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.

The Geometry Of The Universe

Author : Colin Rourke
Publisher : World Scientific
ISBN 13 : 9811233888
Total Pages : 274 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis The Geometry Of The Universe by : Colin Rourke

Download or read book The Geometry Of The Universe written by Colin Rourke and published by World Scientific. This book was released on 2021-06-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cosmology, the study of the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e.g. the 'big bang' and 'black holes') discussed, often in great depth.Accordingly the book is divided into three parts:Part 1 is readable (and understandable) by anyone with a nodding acquaintance with the basic language of cosmology: events, lights paths, galaxies, black holes and so on. It covers the whole story of the book in a way as untechnical as possible given the scope of the topics covered.Part 2 covers the same ground again but with enough technical details to satisfy a reader with basic knowledge of mathematics and/or physics.Part 3 consists of appendices which are referred to in the other parts and which also contain the highly technical material omitted from Section 2.

An Introduction to Riemannian Geometry

Author : Leonor Godinho
Publisher : Springer
ISBN 13 : 3319086669
Total Pages : 467 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Introduction to Riemannian Geometry by : Leonor Godinho

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Introduction to Non-Euclidean Geometry

Author : Harold E. Wolfe
Publisher : Courier Corporation
ISBN 13 : 0486320375
Total Pages : 272 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introduction to Non-Euclidean Geometry by : Harold E. Wolfe

Download or read book Introduction to Non-Euclidean Geometry written by Harold E. Wolfe and published by Courier Corporation. This book was released on 2013-09-26 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.

The Wraparound Universe

Author : Jean-Pierre Luminet
Publisher : CRC Press
ISBN 13 : 1439864969
Total Pages : 400 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis The Wraparound Universe by : Jean-Pierre Luminet

Download or read book The Wraparound Universe written by Jean-Pierre Luminet and published by CRC Press. This book was released on 2008-03-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: What shape is the universe? Is it curved and closed in on itself? Is it expanding? Where is it headed? Could space be wrapped around itself, such that it produces ghost images of faraway galaxies? Such are the questions posed by Jean-Pierre Luminet in The Wraparound Universe, which he then addresses in clear and accessible language. An expert in black holes and the big bang, he leads us on a voyage through the surprising byways of space-time, where possible topologies of the universe, explorations of the infinite, and cosmic mirages combine their mysterious traits and unlock the imagination. The Wraparound Universe is a general-audience book about the overall topology or shape of the universe. The central question addressed is whether it is possible that the universe is wrapped around in an interesting way, and what impact this would have on astronomical observations and our understanding of cosmology. Along the way many of the general features and much of the history of the modern picture of cosmology are discussed.

Noncommutative Geometry and Particle Physics

Author : Walter D. van Suijlekom
Publisher : Springer
ISBN 13 : 9401791627
Total Pages : 237 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Noncommutative Geometry and Particle Physics by : Walter D. van Suijlekom

Download or read book Noncommutative Geometry and Particle Physics written by Walter D. van Suijlekom and published by Springer. This book was released on 2014-07-21 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.

The Shape of Space

Author : Jeffrey R. Weeks
Publisher : CRC Press
ISBN 13 : 0203912667
Total Pages : 405 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis The Shape of Space by : Jeffrey R. Weeks

Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2001-12-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

The Shape of Inner Space

Author : Shing-Tung Yau
Publisher : Il Saggiatore
ISBN 13 : 0465020232
Total Pages : 398 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Shape of Inner Space by : Shing-Tung Yau

Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

An Introduction to Modern Cosmology

Author : Andrew Liddle
Publisher : John Wiley & Sons
ISBN 13 : 1118690273
Total Pages : 200 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis An Introduction to Modern Cosmology by : Andrew Liddle

Download or read book An Introduction to Modern Cosmology written by Andrew Liddle and published by John Wiley & Sons. This book was released on 2015-03-09 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader’s understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology. The accompanying website for this text, http://booksupport.wiley.com, provides additional material designed to enhance your learning, as well as errata within the text.

An Introduction to Machine Learning

Author : Miroslav Kubat
Publisher : Springer Nature
ISBN 13 : 3030819353
Total Pages : 458 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis An Introduction to Machine Learning by : Miroslav Kubat

Download or read book An Introduction to Machine Learning written by Miroslav Kubat and published by Springer Nature. This book was released on 2021-09-25 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a comprehensive introduction to Machine Learning techniques and algorithms. This Third Edition covers newer approaches that have become highly topical, including deep learning, and auto-encoding, introductory information about temporal learning and hidden Markov models, and a much more detailed treatment of reinforcement learning. The book is written in an easy-to-understand manner with many examples and pictures, and with a lot of practical advice and discussions of simple applications. The main topics include Bayesian classifiers, nearest-neighbor classifiers, linear and polynomial classifiers, decision trees, rule-induction programs, artificial neural networks, support vector machines, boosting algorithms, unsupervised learning (including Kohonen networks and auto-encoding), deep learning, reinforcement learning, temporal learning (including long short-term memory), hidden Markov models, and the genetic algorithm. Special attention is devoted to performance evaluation, statistical assessment, and to many practical issues ranging from feature selection and feature construction to bias, context, multi-label domains, and the problem of imbalanced classes.

Geometry, Relativity and the Fourth Dimension

Author : Rudolf Rucker
Publisher : Courier Corporation
ISBN 13 : 0486140334
Total Pages : 159 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Geometry, Relativity and the Fourth Dimension by : Rudolf Rucker

Download or read book Geometry, Relativity and the Fourth Dimension written by Rudolf Rucker and published by Courier Corporation. This book was released on 2012-06-08 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

Lectures on the Geometry of Manifolds

Author :
Publisher :
ISBN 13 : 9814474770
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Lectures on the Geometry of Manifolds by :

Download or read book Lectures on the Geometry of Manifolds written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to General Relativity and Cosmology

Author : Jerzy Plebanski
Publisher : Cambridge University Press
ISBN 13 : 9781107407367
Total Pages : 0 pages
Book Rating : 4.4/5 (73 download)

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Book Synopsis An Introduction to General Relativity and Cosmology by : Jerzy Plebanski

Download or read book An Introduction to General Relativity and Cosmology written by Jerzy Plebanski and published by Cambridge University Press. This book was released on 2012-09-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. Many topics are included that are not found in other textbooks.

Introduction to Hyperbolic Geometry

Author : Arlan Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 9780387943398
Total Pages : 308 pages
Book Rating : 4.9/5 (433 download)

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Book Synopsis Introduction to Hyperbolic Geometry by : Arlan Ramsay

Download or read book Introduction to Hyperbolic Geometry written by Arlan Ramsay and published by Springer Science & Business Media. This book was released on 1995-12-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

Topological Geometrodynamics

Author : Matti Pitkanen
Publisher : Bentham Science Publishers
ISBN 13 : 1681081792
Total Pages : 1235 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis Topological Geometrodynamics by : Matti Pitkanen

Download or read book Topological Geometrodynamics written by Matti Pitkanen and published by Bentham Science Publishers. This book was released on 2016-03-03 with total page 1235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.

Introduction to Topology

Author : Colin Conrad Adams
Publisher : Pearson
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Introduction to Topology by : Colin Conrad Adams

Download or read book Introduction to Topology written by Colin Conrad Adams and published by Pearson. This book was released on 2008 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology.

The Shape of Space

Author : Jeffrey R. Weeks
Publisher : CRC Press
ISBN 13 : 1135542651
Total Pages : 263 pages
Book Rating : 4.1/5 (355 download)

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Book Synopsis The Shape of Space by : Jeffrey R. Weeks

Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2001-12-12 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.